A new numerical strategy with space-time adaptivity and error control for multi-scale streamer discharge simulations

This paper presents a new resolution strategy for multi-scale streamer discharge simulations based on a second order time adaptive integration and space adaptive multiresolution. A classical fluid model is used to describe plasma discharges, considering drift-diffusion equations and the computation of electric field. The proposed numerical method provides a time-space accuracy control of the solution, and thus, an effective accurate resolution independent of the fastest physical time scale. An important improvement of the computational efficiency is achieved whenever the required time steps go beyond standard stability constraints associated with mesh size or source time scales for the resolution of the drift-diffusion equations, whereas the stability constraint related to the dielectric relaxation time scale is respected but with a second order precision. Numerical illustrations show that the strategy can be efficiently applied to simulate the propagation of highly nonlinear ionizing waves as streamer discharges, as well as highly multi-scale nanosecond repetitively pulsed discharges, describing consistently a broad spectrum of space and time scales as well as different physical scenarios for consecutive discharge/post-discharge phases, out of reach of standard non-adaptive methods.Comment: Support of Ecole Centrale Paris is gratefully acknowledged for several month stay of Z. Bonaventura at Laboratory EM2C as visiting Professor. Authors express special thanks to Christian Tenaud (LIMSI-CNRS) for providing the basis of the multiresolution kernel of MR CHORUS, code developed for compressible Navier-Stokes equations (D\'eclaration d'Invention DI 03760-01). Accepted for publication; Journal of Computational Physics (2011) 1-2

Gaussian process regression for virtual metrology of microchip quality and the resulting strategic sampling scheme

Manufacturing of integrated circuits involves many sequential processes, often ex- ecuted to nanoscale tolerances, and the yield depends on the often unmeasured quality of intermediate steps. In the high-throughput industry of fabricating microelectronics on semi-conducting wafers, scheduling measurements of product quality before the electrical test of the complete IC can be expensive. We therefore seek to predict metrics of product quality based on sensor readings describing the environment within the relevant tool during the processing of each wafer, or to apply the concept of virtual metrology (VM) to monitor these intermediate steps. We model the data using Gaussian process regression (GPR), adapted to simultaneously learn the nonlinear dynamics that govern the quality characteristic, as well as their operating space, expressed by a linear embedding of the sensor traces’ features. Such Bayesian models predict a distribution for the target metric, such as a critical dimension, so one may assess the model’s credibility through its predictive uncertainty. Assuming measurements of the quality characteristic of interest are budgeted, we seek to hasten convergence of the GPR model to a credible form through an active sampling scheme, whereby the predictive uncertainty informs which wafer’s quality to measure next. We evaluate this convergence when predicting and updating online, as if in a factory, using a large dataset for plasma-enhanced chemical vapor deposition (PECVD), with measured thicknesses for ~32,000 wafers. By approximately optimizing the information extracted from this seemingly repetitive data describing a tightly controlled process, GPR achieves ~10% greater accuracy on average than a baseline linear model based on partial least squares (PLS). In a derivative study, we seek to discern the degree of drift in the process over the several months the data spans. We express this drift by how unusual the relevant features, as embedded by the GPR model, appear as the in- puts compensate for degrading conditions. This method detects the onset of consistently unusual behavior that extends to a bimodal thickness fault, anticipating its flagging by as much as two days.Mechanical Engineerin

The effects of noise on binocular rivalry waves: a stochastic neural field model

We analyse the effects of extrinsic noise on traveling waves of visual perception in a competitive neural field model of binocular rivalry. The model consists of two one-dimensional excitatory neural fields, whose activity variables represent the responses to left-eye and right-eye stimuli, respectively. The two networks mutually inhibit each other, and slow adaptation is incorporated into the model by taking the network connections to exhibit synaptic depression. We first show how, in the absence of any noise, the system supports a propagating composite wave consisting of an invading activity front in one network co-moving with a retreating front in the other network. Using a separation of time scales and perturbation methods previously developed for stochastic reaction-diffusion equations, we then show how multiplicative noise in the activity variables leads to a diffusive–like displacement (wandering) of the composite wave from its uniformly translating position at long time scales, and fluctuations in the wave profile around its instantaneous position at short time scales. The multiplicative noise also renormalizes the mean speed of the wave. We use our analysis to calculate the first passage time distribution for a stochastic rivalry wave to travel a fixed distance, which we find to be given by an inverse Gaussian. Finally, we investigate the effects of noise in the depression variables, which under an adiabatic approximation leads to quenched disorder in the neural fields during propagation of a wave

Adaptive time splitting method for multi-scale evolutionary partial differential equations

Accepted to publication in Confluentes Mathematici. Dedication : Cet article est dédié à la mémoire de Michelle Schatzman. Spécialiste des méthodes de décomposition d'opérateur, sa grande clairvoyance scientifique lui a permis d'orienter plusieurs chercheurs débutants sur ce sujet à un moment où il pouvait sembler achevé. Michelle aimait dire qu'il n'y a pas de frontière entre les branches des mathématiques et que seule une grande culture permet de naviguer dans cette forêt et d'y trouver les bonnes techniques pour résoudre un problème. Ce travail est un hommage; à la croisée des mathématiques et de leurs applications effectives, il tente d'illustrer cette assertion. Michelle, ton dynamisme, ton humour et ton plaisir à parler mathématiques nous manquent.International audienceThis paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady problems. The strategy considers a second order Strang method and another lower order embedded splitting scheme that takes into account potential loss of order due to the stiffness featured by time-space multi-scale phenomena. The scheme is then built upon a precise numerical analysis of the method and a complementary numerical procedure, conceived to overcome classical restrictions of adaptive time stepping schemes based on lower order embedded methods, whenever asymptotic estimates fail to predict the dynamics of the problem. The performance of the method in terms of control of integration errors is evaluated by numerical simulations of stiff propagating waves coming from nonlinear chemical dynamics models as well as highly multi-scale nanosecond repetitively pulsed gas discharges, which allow to illustrate the method capabilities to consistently describe a broad spectrum of time scales and different physical scenarios for consecutive discharge/post-discharge phases

The prodrome of autism: early behavioral and biological signs, regression, peri- and post-natal development and genetics

Autism is one of the most heritable neurodevelopmental conditions and has an early onset, with symptoms being required to be present in the first 3 years of life in order to meet criteria for the ‘core’ disorder in the classification systems. As such, the focus on identifying a prodrome over the past 20 years has been on pre-clinical signs or indicators that will be present very early in life, certainly in infancy. A number of novel lines of investigation have been used to this end, including retrospective coding of home videos, prospective population screening and ‘high risk’ sibling studies; as well as the investigation of pre- and peri-natal, brain developmental and other biological factors. Whilst no single prodromal sign is expected to be present in all cases, a picture is emerging of indicative prodromal signs in infancy and initial studies are being undertaken to attempt to ameliorate the early presentation and even ‘prevent’ emergence of the full syndrome

Habit reversal therapy in obsessive compulsive related disorders : A systematic review of the evidence and consort evaluation of randomized controlled trials

Background: Habit Reversal Therapy (HRT) has long been used in the treatment of Tourette Syndrome and Tic Disorders. It has more recently been used to treat Trichotillomania and skin picking behaviors, both considered as Obsessive Compulsive Related Disorders (OCRD). Objectives: This literature review sought to establish and quality assess the existing randomized controlled trial evidence supporting the use of HRT in the DSM-5 family of OCRDs. Search Methods: EMBASE, PsycINFO, PubMed, and Cochrane databases were searched for key terms relating to each OCRD (as classified in the DSM-5), and HRT. Selection Criteria: Titles and abstracts were screened, and any literature matching pre-specified criteria were then selected to be reviewed further. Of these, 8 Randomized Controlled Trials (RCT) relating to Trichotillomania, and 2 RCTs relating to Excoriation Disorder, were extracted and reviewed against the 2010 Consolidating Standards of Reporting Trials (CONSORT) statement. Results: The review identified 10 RCTs of HRT, but these were limited to patients with a primary diagnosis of Trichotillomania or “excoriation behavior,” only. There were some reports of the use of HRT in Tourette Syndrome or Tic Disorder with secondary OCD, but the OCD symptoms were not reliably reported on. Conclusion: There is a gap in the current literature regarding the use of HRT in the DSM-5 OCRDs. In those RCTs that have been reported, the quality of study methodology was questionable as evaluated by CONSORT criteria. The implications of these findings are discussed, and suggestions are made for future research.Peer reviewe

The Repetitive Behavior Spectrum in Autism and Obsessive Compulsive Disorder: From Helpful to Harmful

Systematic study comparing repetitive behaviors in autism with those observed in obsessive compulsive disorder (OCD) and other Diagnostic and Statistical Manual of Mental Disorders- Fourth Edition-Text Revision (DSM-IV-TR) diagnoses is lacking despite its diagnostic and treatment significance. This research examines repetitive behaviors in a sample of children and adults diagnosed with an autism spectrum disorder (ASD), (OCD), or both. Data were collected from three participant pools; clinic clients, parents/caregivers, and therapists; in order to test the psychometric properties of questions for assessing the functional characteristics of repetitive thoughts and behavior (i.e., stereotypy, compulsion, obsession, perseveration, preoccupation). Exploratory factor analyses revealed four factors that demonstrated reasonable consistency across the three types of informants. These four assessed factors included: 1) intrusive effects; 2) soothing effects; 3) level of distress, and; 4) pleasure-seeking qualities. Reliability for the new scales was calculated separately for subjects, correspondents, and therapists revealing high internal consistency. Validity analyses were completed, first by examining bivariate correlations among the new scales and then by examining correlations between the new scales and then by examining correlations between the new scales and established measures of functioning (i.e., Gilliam Autism Rating Scale-Second Edition; GARS-2, Yale-Brown Obsessive Compulsive Scale; Y-BOCS, and Adaptive Behavior Assessment System-Second Edition; ABAS-II). As hypothesized, the new scales measuring soothing and pleasure-seeking qualities of repetitive behavior had higher correlations with measures of ASD than OCD and the new scales measuring level of distress and intrusiveness in repetitive behavior had higher correlations with measures of OCD than ASD. The results of this study take a step toward better distinguishing what motivates repetitive behaviors and, thus, how to best think about them in the context of intervention strategies